Skip to main content

Advertisement

Log in

From here to there! Elementary: a game-based approach to developing number sense and early algebraic understanding

  • Development Article
  • Published:
Educational Technology Research and Development Aims and scope Submit manuscript

Abstract

This paper examines whether using From Here to There! (FH2T:E), a dynamic game-based mathematics learning technology relates to improved early algebraic understanding. We use student log files within FH2T to explore the possible benefits of student behaviors and gamification on learning gains. Using in app measures of student interactions (mouse clicks, resets, errors, problem solving steps, and completions), 19 variables were identified to summarize overall problem solving processes. An exploratory factor analysis identified five clear factors including engagement in problem solving, progress, strategic flexibility, strategic efficiency, and speed. Regression analyses reveal that after accounting for behavior within the app, playing the gamified version of the app contributed to higher learning gains than playing a nongamified version. Next, completing more problems within the game related to higher achievement on the post-test. Third, two significant interactions were found between progress and prior knowledge and engagement in problem solving and prior knowledge, where low performing students gained more when they completed more problems and engaged more with those problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 1–34). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Bay-Williams, J. M. (2001). What is algebra in elementary school? Teaching Children Mathematics, 8(4), 196–200. http://www.jstor.org.ezproxy.wpi.edu/stable/41197754.

  • Blanton, M., Stephens, A., Knuth, E., Angela, M. G., Isler, I., & Kim, Jee-Seon. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039.

    Article  Google Scholar 

  • Booth, J. L., Barbieri, C., Eyer, F., & Par-Blagoev, E. J. (2014). Persistent and pernicious errors in algebraic problem solving. Journal of Problem Solving, 7(1), 3.

    Article  Google Scholar 

  • Braith, L., Daigle, M., Manzo, D., & Ottmar, E. (2017). Even elementary students can explore algebra! Testing the feasibility of From Here to There!, a game-based perceptual learning intervention. Poster presented at the American Psychological Society Conference, Boston, Massachusetts.

  • Bransford, J. D., & Schwartz, D. L. (1999). Chapter 3: Rethinking transfer: A simple proposal with multiple implications. Review of Research in Education, 24(1), 61–100.

    Article  Google Scholar 

  • Bruner, J., Olver, R., & Greenfield, P. (1966). Studies in cognitive growth: A collaboration at the center for cognitive studies. New York: Wiley.

    Google Scholar 

  • Carpenter, T., Levi, L., Franke, M., & Zeringue, J. (2005). Algebra in elementary school: Developing relational thinking. Zentralblatt Für Didaktik Der Mathematik, 37(1), 53–59. https://doi.org/10.1007/BF02655897.

    Article  Google Scholar 

  • Carr, M., Taasoobshirazi, G., Stroud, R., & Royer, J. M. (2011). Combined fluency and cognitive strategies instruction improves mathematics achievement in early elementary school. Contemporary Educational Psychology, 36(4), 323–333.

    Article  Google Scholar 

  • Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. Second Handbook of Research on Mathematics Teaching and Learning, 2, 669–705.

    Google Scholar 

  • Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37, 87–115.

    Google Scholar 

  • Cayton-Hodges, G. A., Feng, G., & Pan, X. (2015). Tablet-based math assessment: What can we learn from math apps? Educational Technology & Society, 18(2), 3–20.

    Google Scholar 

  • Chudowsky, N., & Pellegrino, J. W. (2003). Large-scale assessments that support learning: What will it take? Theory into Practice, 42(1), 75–83.

    Article  Google Scholar 

  • Clark, D. B., Tanner-Smith, E. E., & Killingsworth, S. S. (2016). Digital games, design, and learning: A systematic review and meta-analysis. Review of Educational Research, 86(1), 79–122.

    Article  Google Scholar 

  • Clements, D. H. (2000). ‘Concrete’ manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45–60.

    Article  Google Scholar 

  • Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38, 136–163.

    Google Scholar 

  • Common Core State Standards Initiative (CCSSI) (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.

  • Cortes, K. E., Goodman, J. S., & Nomi, T. (2015). Intensive math instruction and educational attainment long-run impacts of double-dose algebra. Journal of Human Resources, 50(1), 108–158.

    Article  Google Scholar 

  • Doig, B., & Ompok, C. (2010). Assessing young children’s mathematical abilities through games. Procedia - Social and Behavioral Sciences, 8, 228–235. https://doi.org/10.1016/j.sbspro.2010.12.031.

    Article  Google Scholar 

  • Drasgow, F. (Ed.). (2015). Technology and testing: Improving educational and psychological measurement. Routledge.

  • Field, A. P. (2009). Discovering statistics using SPSS (3rd ed.). Los Angeles: Sage.

    Google Scholar 

  • Gee, J. P. (2003). What video games have to teach us about learning and literacy. Computers in Entertainment (CIE), 1(1), 20.

    Article  Google Scholar 

  • Gobert, J. D., Sao Pedro, M., Raziuddin, J., & Baker, R. S. (2013). From log files to assessment metrics: Measuring students’ science inquiry skills using educational data mining. Journal of the Learning Sciences, 22(4), 521–563.

    Article  Google Scholar 

  • Goldstone, R., Landy, D., & Brunel, L. C. (2011). Improving perception to make distant connections closer. Frontiers in Psychology, 2 385.

    Article  Google Scholar 

  • Goldstone, R. L., Landy, D. H., & Son, J. Y. (2010). The education of perception. Topics in Cognitive Science, 2(2), 265–284.

    Article  Google Scholar 

  • Hutcheson, G. D., & Sofroniou, N. (1999). The multivariate social scientist: Introductory statistics using generalized linear models. Los Angeles: Sage.

    Book  Google Scholar 

  • Jere-Folotiya, J., Chansa-Kabali, T., Munachaka, J. C., Sampa, F., Yalukanda, C., Westerholm, J., et al. (2014). The effect of using a mobile literacy game to improve literacy levels of grade one students in zambian schools. Educational Technology Research and Development, 62(4), 417–436.

    Article  Google Scholar 

  • Kalchman, M. (2011). Using the math in everyday life to improve student learning: The Math in Everyday Life homework assignment builds student confidence and competence in mathematics. Middle School Journal, 43(1), 24–31.

    Article  Google Scholar 

  • Kalyuga, S. (2009). Knowledge elaboration: A cognitive load perspective. Learning and Instruction, 19(5), 402–410.

    Article  Google Scholar 

  • Kellman, P. J., Massey, C. M., & Son, J. Y. (2010). Perceptual learning modules in mathematics: Enhancing students’ pattern recognition, structure extraction, and fluency. Topics in Cognitive Science, 2(2), 285–305.

    Article  Google Scholar 

  • Kiili, K., Devlin, K., Perttula, T., Tuomi, P., & Lindstedt, A. (2015). Using video games to combine learning and assessment in mathematics education. International Journal of Serious Games, 2(4), 37–55.

    Google Scholar 

  • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312.

    Google Scholar 

  • Koedinger, K. R., Alibali, M. W., & Nathan, M. J. (2008). Trade-offs between grounded and abstract representations: Evidence from algebra problem solving. Cognitive Science, 32(2), 366–397.

    Article  Google Scholar 

  • Lins, R., & Kaput, J. (2004). The early development of algebraic reasoning: The current state of the field. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 47–70).

  • Moyer-Packenham, P. S., & Suh, J. M. (2012). Learning mathematics with technology: The influence of virtual manipulatives on different achievement groups. Journal of Computers in Mathematics and Science Teaching, 31(1), 39–59.

    Google Scholar 

  • National Council of Teachers of Mathematics, Inc (NCTM). (2000). Standards for grades Pre-K-2. Principles and standards for school mathematics (Vol. 1, pp. 72–141).

  • National Council of Teachers of Mathematics. (2014). Algebra as a strand of school mathematics for all students: A position of the national council of teachers of mathematics. Retrieved from https://www.nctm.org/uploadedFiles/Standards_and_Positions/Position_Statements/Algebra_2014-04.pdf.

  • National Mathematics Advisory Panel (NMAP). (2008). https://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.

  • National Research Council. (2001). Knowing what students know: The science and design of educational assessment. In J.W. Pellegrino, N. Chudowsky, & R. Glaser (Eds.). Washington, DC: National Academies Press.

  • Ottmar, E., & Landy, D. (2017). Concreteness fading of algebraic instruction: Effects on learning. Journal of the Learning Sciences, 26(1), 51–78.

    Article  Google Scholar 

  • Ottmar, E., Landy, D., & Goldstone, R. L. (2012). Teaching the perceptual structure of algebraic expressions: Preliminary findings from the pushing symbols intervention. The Proceedings of the Thirty-Fourth Annual Conference of the Cognitive Science Society, 2156–2161.

  • Ottmar, E. R., Landy, D., Goldstone, R., & Weitnauer, E. (2015). Getting from here to there! Testing the effectiveness of an interactive mathematics intervention embedding perceptual learning. Proceedings of the 37th Annual Conference of the Cognitive Science Society.

  • Schoenfeld, A. H. (2007). Assessing mathematical proficiency (Vol. 53). Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Seitz, A., & Watanabe, T. (2005). A unified model for perceptual learning. Trends in cognitive sciences, 9(7), 329–334.

    Article  Google Scholar 

  • Shute, V. J. (2011). Stealth assessment in computer-based games to support learning. Computer games and instruction, 55(2), 503–524.

    Google Scholar 

  • Sowder, J. T. (1992). Making sense of numbers in school mathematics. In G. Leinhardt, R. Putnam, & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 1–46). East Sussex: Psychology Press.

    Google Scholar 

  • Stein, M. K., Kaufman, J. H., Sherman, M., & Hillen, A. F. (2011). Algebra: A challenge at the crossroads of policy and practice. Review of Educational Research, 81(4), 453–492.

    Article  Google Scholar 

  • Stephens, A., Blanton, M., Knuth, E., Isler, I., & Gardiner, A. M. (2015). Just say yes to early algebra! Teaching Children Mathematics, 22(2), 92–101.

    Article  Google Scholar 

  • Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Boston: Pearson.

    Google Scholar 

  • VanDerHeyden, A. M., & Burns, M. K. (2009). Performance indicators in math: Implications for brief experimental analysis of academic performance. Journal of Behavioral Education, 18(1), 71–91.

    Article  Google Scholar 

  • Welder, R. M. (2012). Improving algebra preparation: Implications from research on student misconceptions and difficulties. School Science and Mathematics, 112(4), 255–264.

    Article  Google Scholar 

  • Wouters, P., Van Nimwegen, C., Van Oostendorp, H., & Van Der Spek, Erik D. (2013). A meta-analysis of the cognitive and motivational effects of serious games. American Psychological Association.

Download references

Acknowledgments

The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant No. R305A110060 to University of Richmond and Indiana University. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education. The authors are also grateful to the many teachers and students who helped make this research possible.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Erin Ottmar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hulse, T., Daigle, M., Manzo, D. et al. From here to there! Elementary: a game-based approach to developing number sense and early algebraic understanding. Education Tech Research Dev 67, 423–441 (2019). https://doi.org/10.1007/s11423-019-09653-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11423-019-09653-8

Keywords

Navigation